THE SUPER-BIHAMILTONIAN REDUCTION ON C∞(S1, OSP(1|2))

doi:10.1016/S0252-9602(14)60026-6

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (2): 537-545.doi: 10.1016/S0252-9602(14)60026-6

THE SUPER-BIHAMILTONIAN REDUCTION ON C^∞(S¹, OSP(1|2))

张玲|左达峰

Department of Mathematics, Chuzhou University, Chuzhou 239012, China；School of Mathematical Science, University of Science and Technology of China, Hefei 230026, China； School of Mathematical Science, University of Science and Technology of China, Hefei 230026, China；Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences

收稿日期:2012-12-12 修回日期:2013-05-21 出版日期:2014-03-20 发布日期:2014-03-20
基金资助:
This work is partially supported by “PCSIRT”; the Fundamental Research Funds for the Central Universities (WK0010000024); NCET-13-0550; SRF for ROCS, SEM and OATF, USTC; NSFC (11271345, 11371138); Natural Science Foundation of Anhui Province and Outstanding Young Talent Funds of Anhui Province (2013SQRL092ZD).

THE SUPER-BIHAMILTONIAN REDUCTION ON C^∞(S¹, OSP(1|2))

ZHANG Ling, ZUO Da-Feng

Department of Mathematics, Chuzhou University, Chuzhou 239012, China；School of Mathematical Science, University of Science and Technology of China, Hefei 230026, China； School of Mathematical Science, University of Science and Technology of China, Hefei 230026, China；Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences

Received:2012-12-12 Revised:2013-05-21 Online:2014-03-20 Published:2014-03-20
Supported by:
This work is partially supported by “PCSIRT”; the Fundamental Research Funds for the Central Universities (WK0010000024); NCET-13-0550; SRF for ROCS, SEM and OATF, USTC; NSFC (11271345, 11371138); Natural Science Foundation of Anhui Province and Outstanding Young Talent Funds of Anhui Province (2013SQRL092ZD).

摘要/Abstract

摘要：

In this article, we will show that the super-bihamiltonian structures of the Kuper-KdV equation in [3], the Kuper-CH equation in [17, 18] and the super-HS equation in [11, 16, 19] can be obtained by applying a super-bihamiltonian reduction of different super-Poisson pairs defined on the loop algebra of osp(1|2).

关键词: Super-bihamiltonian reduction, loop algebra of osp(1, 2)

Abstract:

Key words: Super-bihamiltonian reduction, loop algebra of osp(1, 2)

中图分类号:

37K10

张玲, 左达峰. THE SUPER-BIHAMILTONIAN REDUCTION ON C^∞(S¹, OSP(1|2))[J]. 数学物理学报(英文版), 2014, 34(2): 537-545.

ZHANG Ling, ZUO Da-Feng. THE SUPER-BIHAMILTONIAN REDUCTION ON C^∞(S¹, OSP(1|2))[J]. Acta mathematica scientia,Series B, 2014, 34(2): 537-545.

参考文献

[1] Kac V. Lie superalgebras. Advances in Math, 1977, 26: 8–96

[2] Drinfeld V G, Sokolov V V. Lie algebras and Equations of Korteweg-de Vries type. J Sov Math, 1985, 30: 1975–2036

[3] Kupershmidt B A. A super Korteveg-de Vries equation: an integrable system. Phys Lett A, 1984, 102: 213–215

[4] Marsden J E, Ratiu T. Reduction of Poisson Manifolds. Lett Math Phys, 1986, 11: 161–169

[5] Ovsienko V Yu, Khesin B. The (super) KdV equation as an Euler equation. Funct Anal Appl, 1987, 21: 329–331

[6] Casati P, Magri F, Pedroni M. BiHamiltonian manifolds and the -function//Gotai M, Marsden J, Moncrief V. Proceedings of the 1991 Joint Summer Research Conference on Mathematical aspects of Classical Field Theory. Contemporary Math, 1992, 132: 213–234

[7] Casati P, Pedroni M. Drinfeld-Sokolov reduction on a simple Lie algebra from the biHamiltonian point of view. Lett Math Phys, 1992, 25: 89–101

[8] Morosi C, Pizzocchero L. On the BiHamiltonian Structure of the Supersymmetric KdV Hierarchies: A Lie
Superalgebraic Approach. Commun Math Phys, 1993, 158: 267–288

[9] Delduc F, Gallot L. Supersymmetric Drinfeld-Sokolov reduction. J Math Phys, 1998, 39: 4729–4745

[10] Devchand C, Schiff J. The supersymmetric Camassa-Holm equation and geodesic flow on the superconformal
group. J Math Phys, 2001, 1: 260–273

[11] Brunelli J C, Das A, Popowicz Z. Supersymmetric extensions of the Harry Dym hierarchy. J Math Phys, 2003, 44: 4756–4767

[12] Khesin B, Misiolek G. Euler equations on homogeneous spaces and Virasoro orbits. Adv Math, 2003, 176: 116–144

[13] Lorenzoni P, Pedroni M. On the bi-Hamiltonian structures of the Camassa-Holm and Harry Dym equations. Int Math Res Not, 2004, 75: 4019–4029

[14] Kulish P P, Zeitlin A M. Group-theoretical structure and inverse scattering method for super-KdV equation. Journal of Mathematical Sciences, 2005, 2: 203–214

[15] Fontanelli L, Lorenzoni P, Pedroni M, Zubelli J P. Bi-Hamiltonian aspects of a matrix Harry Dym hierarchy. J Math Phys, 2008, 49: 092901, 15pp

[16] Lenells J. A bi-Hamiltonian supersymmetric geodesic equation. Lett Math Phys, 2008, 85: 55–63

[17] Zuo D. Euler equations related to the generalized Neveu-Schwarz algebra. SIGMA, 2013, 9(45): 12page

[18] Zhang L, Zuo D. Integrable hierarchies related to the Kuper-CH spectral problem. J Math Phys, 2011, 52: 073503

[19] Zhang L, Zuo D. Two supersymmetric hierarchies related to the super-HS spectral problem. Commun. Nonlinear Sci Numer Simul, 2013, 18: 257–263

THE SUPER-BIHAMILTONIAN REDUCTION ON C^∞(S¹, OSP(1|2))

THE SUPER-BIHAMILTONIAN REDUCTION ON C^∞(S¹, OSP(1|2))

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